Question

Calculate the sum of even numbers between $12$ and $90$ which are divisible by $8$.

• A. $500$
• B. $510$
• C. $520$
• D. $620$

Answer 1

Answer: (C)

$520$

The list of odd numbers between $12$ and $90$ which are divisible by $8$ are $16,24,.....88$

The sum of first $n$ terms of arithmetic series formula can be written as,

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)

Where $n=$ number of terms = ?

$a=$ first odd number $=16$

$d=$ common difference of A.P. $=8$

$T_n=$ Last term $=88$

$T_n=a+(n-1)d$

$88=16+(n-1)8$

$88=16+8n-8$

$88-16+8=8n$

$80=8n$

$n=10$

Apply the given data in the formula (1),

$S_{10}=\frac{10}{2}[2\times 16+(10-1\left)8\right]$

$=5[32+(9\left)8\right]$

$=5[32+72]$

$=5\left[104\right]$

$=520$

So, the sum of even numbers between $12$ and $90$ which are divisible by $8$ is $520$.